Well, I put them all together. Basil, his two sisters (all just at the fag-end of their breeding age) and his daughter. They were in for about three weeks and then I took him out.
Not one of them conceived as far as I can tell. Another few weeks down the line and no sign of anything.Eventually I caved in and inspected the girls' nest, but no sign of anything present or deceased.
So... if the older mice are post-menopause and the daughter is infertile, can they all go in together with Basil?
Ask not what your rodent can do for you...